It is trivial from [1]} that if \(f\)  is differentiable for \(\mathfrak {m}\) -a.e. \(x \in A\)  with \(\mathfrak {m}(X \setminus A)=0\) , then \(\nabla f\)  is well-defined in \(L^0(TX)\) , that is, \(\nabla f\)  is a Borel measurable vector field on \(X\) .
